Method for controlling operations for the cooling of steel plate in accordance with formulae obtained by theoretical analysis



Jan. 23, 1968 NOBUO FUKUDA ET AL 3,364,713

METHOD FOR CONTROLLING OPERATIONS FOR THE COOLING OF STEEL PLATE INACCORDANCE WITH FORMULAE OBTAINED BY THEORETICAL ANALYSIS Filed Aug. 26,1964 *Signal bf operation stoppage due in over capacity K apparatus QWater I showering Si nal of o erac P3. V In 9F-9w)'/, Q 020mm Q Qma n31stoppage due q- 9C 2 to under oapacify FIG. I

lemperature 450 l l l l l I INVENTORS 450 500 550 600 e50 700 750 NobuoFukuda Calculated iemperafure (C) ralliuya Kimuta K011 Wu da BY Maw? WMATTORNEYS United States Patent 3 364,713 It-ZETHOD FOR CONTliOLLiNGOPERATIONS FUR THE COQLENG 'Jl STEEL PLATE IN ACCURD- ANCE WlTH FORMULAEOBTAHNED BY THEO- RETlCAL ANALYSlS Nobuo Fultuda and Tatsuya Kimnra,Kitaiq'ushu, and Koii Wade, Sairai, Japan, assignors to Yawata Iron 8:Steel (10., Ltd, Tokyo, Japan, a corporation of Japan Filed Aug. 26,1964, Ser. No. 392,248 Claims priority, application Japan, Aug. 27,1963, 38/ 25,134 3 Claims. (Cl. 722G1) ABSTRACT OF THE DESCLQSURE Amethod for predictive control of the coiling temperature of steel stripdelivered from the finishing stands of a hot strip mill, in which use ismade of rolling speed, finishing temperature, strip thickness, watertemperature, physical constants (specific heat, specific weight andemissivity) of rolled material, and, initial settings of sprayinglocation and valve opening for cooiing water; with these factors acoiling temperature is computed and compared with the desired coilingtemperature. If the computed temperature is higher than the desiredtemperature, the spraying portion of the cooling apparatus is lengthenedand further the valve opening is widened automatically until thetemperature difference is eliminated. If the computed temperature islower than the desired temperature, the opposite procedure is carriedout.

This invention relates in general to a method for the cooling of steelplate in a hot strip mill, and more particularly to that for controllingoperations for the cooling of steel strip (hereinafter called Ztrip) onthe hotrun table of a hot strip mill in accordance with formulae whichare obtained by theoretical analysis.

In the present hot strip steel plate market, improvement of quality andreduction of production cost are dire necessities. It is therefore anurgent necessity for strip producers to follow the trend in the world tomodernize their hot strip mills by adopting automatic control systems,particularly such systems using computors. This invention is to carryout a method for controlling operations for the cooling of strip on thehot-run table in accordance with formulae which are obtained bytheoretical analysis of the coo-ling conditions of strip, saidconditions having a close relation the improvement of quality of theproduct, thereby developing a new use for an automatic control systemusing computers and also raising the accuracy of operations for thecooling of strip.

Thus this invention is to control and adjust operations for the coolingof strip in accordance with formulae which are obtained by theoreticalanalysis of the two varieties of the cooling process to be carried outafter the rolling process, that is, the cooling by heat conduction byusing a water shower and by heat radiation without using water shower.

The invention will now be described with reference to the accompanyingdrawings in which:

FIG. 1 illustrates the results of these operations mentioned in Table 1.It is noted that good agreement is found between actual coilingtemperatures and coiling temperatures calculated from the formulae.

FIG. 2 is a block diagram according to which the automatic control ofcooling operations is carried out on the hot-run table.

(A) Cooling by heat conduction Vhen strip is cooled by such liquids aswater, heat transfer between the strip and the liquid takes place on thesurface of strip, causing a drop of the temperature of strip. While thesurface is quickly cooled, the cooling of the interior lags behind, andthere must be the difference in temperature drop between the surface andthe interior of strip. However, one may neglect such difference becauseof the thinness of the strip and also its good heat conductivity.(According to the theoretical calculations, the difference oftemperature between the surface of the interior of strip of less than 10mm. thick is not more than one percent, which value is negligiblepractically.)

In the following equations:

0=temperature of strip C.)

0 =temperature of cooling liquid C.)

a=heat transfer coefiicient between strip and cooling liquid (Kcal./m.hr. C.)

C=specific heat of strip (Kcal/kg. C.)

=specific Weight of strip (kg/Nmfi) h=thickness of strip (m.)

t=time (hr.)

The heat transmission between cooling liquid and strip can be expressedby the following differential equation:

2m(90 )dI=Chpd0 (1) Integrating Eq. 1 between i=0 and t=T, one obtains20/1 0 9 e Cp l w) w or rearranging in series function to obtain anapproximate equation where 6 is the temperature of strip before beingcooled by liquid C.); 9 the temperature of strip after cooling C); e thebase of natural logarithm. If strip is to be cooled while travellingover the distance Lm at the velocity Vm/hn, the time required for thiscooling T can be expressed by T=L/ V.

(B) Cooling by heat radiation When the temperature of strip falls due toheat radiation, the temperature drop varies according to the ratiobetween the temperature of the strip and that of the surroundings.Assuming the fourth power of this ratio to be constant (the inventorbelieves that this assumption will result in a practically negligibleerror, if any), the temperature drop due to cooling by heat radiationcan be expressed by the following differential equation.

in this equation =temperature of strip K.)

1 =surrounding temperature coefficient (surrounding temp./ strip temp.)

C=specific heat of strip (Keel/kg. C.)

=speciiic weight of strip (Kcal./Nm.

hzthickness of strip (m.)

azernissivity of strip surface C =Stefan-Baltzmann constant; 4.88KcaL/m. hr.

2C l1(/10O) '(1--')7 )dt=C'h-p'd (4) Assuming 11 to be constant andintegrating Eq. 4 between t=0 and i=1", one obtains where is thetemperature of the strip before being cooled by radiation K), is thetemperature of strip after cooled by radiation K.) where If strip is tobe cooled while travelling over the distance Lm, the time required forthis cooling T can be expressed by T =L/ V.

(C) Application of the above two formulae As part of the operation ofthe hot strip mill, the cooling of strip which is sent from thefinishing mill is carried out on the hot-run table to obtain therequired coiling temperature. This cooling operation is carried out invariations according to types of cooling apparatus and grades and sizesof strip. In any case, the operation can be controlled and adjusted inaccordance with varied cornbinations of the Formulae 2 or 3 and 5.

The following is one example of the calculation of the coilingtemperature of strip which is subjected to cooling by water showeringthroughout the part L m and by radiation throughout the part L m of thehot-run table. (L=L +L The total length of hot-run table is Lm.)

The nomenclature for various temperatures etc:

=Temperature at the end point of the finishing roller (or at the inletinto the water showering part) C.)

e -Temperature at the outlet from the water showering part (or at theinlet into the radiation cooling part) i 9 Temperature at the outletfrom the radiation cooling part (or coiling temperature) C.)

The same nomenclature as mentioned above will be used for the othersymbols. From Eq. 2, one obtains In Eqs. 6 and 7, if the grade and sizeof strip are determined, c, p, h and K will be determined. H will begiven from the rolling conditions, a and B from conditions of theapparatus; 1 from the surrounding conditions. Using these values theFormula 6 can be solved. By applying the results obtained from thiscalculation to Eq. 7, the coiling temperature can be easily obtained. Ifboth 0 1 and 9 are given in the above calculations, one has only to findthe values of L and L which will satisfy simultaneous conditions forEqs. 6 and 7. In case the length of the water showering part is constantand both 6 1 and 9 are given, one has only to find the value of a'.which will satisfy simultaneous conditions for Eqs. 6 and 7, and thenapply this value to a process for controlling the flow rate of the watershower (or the pressure of the water shower). In other practices such ascooling by liquid in a limited part or the latter part of the hotruntable, a combination of the Formulae 2 (or 3) and 5 is applicable invariations. In case of cooling by liquid throughout the whole length ofthe hot-run table only the Formula 2 or 3 will meet the purpose; in caseno such cooling is used on the hot-run table, only the Formula 5 willdo.

Example 1.Comparison of values obtained by the method of this inventionand those obtained from experience Table 1 shows the results ofexperiments which were conducted in accordance with the method of thisinvention for controlling and adjusting operations for the cooling ofstrip of low carbon steel under the following conditions:Stefan-Boltzmann constant C =4.88 Kcal./rn. hr. K./100)*; constants ofstrip C=Gil5 KcaL/kg. C., a=- 0.80 and =7.85 1i) l g./m. constant of thesurrounding conditions #:004; constant of the apparatus L:L +L =80 in.(L represents the length of the water cooling part and L; that of theradiation cooling part); and or in two levels, that is, 10 leg/cm. and4.5 lag/cm.

of water shower pressure. (Besides this, cooling without using a watershower was carried out.)

FIG. 1 illustrates the results of experiments mentioned in Table 1.These show that values calculated by the method of this invention agreealmost exactly with those obtained from experience.

Example 2.Application of the method of this invention to coolingoperations under the automatic control system using computers Accordingto the method of this invention, a cooling operation on the hot-runtable can be controlled without difiiculty by using computers. Oneexample of such operations is shown in FIG. 2. This is a block diagramillustrating operations on such a type of the hotrun table that itswater showering apparatus covers the whole length of the table and isdivided into eight parts.

The nomenclature for constants, parameters and measured values appearingin this block diagraminput:

Constants:

a=Emissivity c Speccific heat =Specific weight 6:1 Coeiiicient ofsurrounding temperature Q =Maximum opening of valve Q =Minimum openingof valve Lu=Length of water showering section unit o Temperature atoutlet finishing mill 9 =Coiling temperature h Thickness of stripZ=Water showering starting section K=Water showering ending sectionQ=Opening of valve q Coefiicient of valve opening u=Exponent of valveopening Measured values:

0 =Temperature of water shower V=Strip speed This block diagram is sodesigned that the location of the water shower can be determined so asto meet metallurgical requirements regarding cooling operations on thehot-run table thereby to reduce the temperature of strip just sent fromthe finishing mills to the desired coiling temperature. Therefore, it ispossible to determine the location of the water shower by figuring l andK. it is also possible to determine the desired initial opening and themaximum and minimum openings of the valve. These are symbolized as Q, Qand Q in FIG. 2. The diagram is also so designed that the values of C, pand a can be changed according to grades of strip. The value of h alsocan be changed according to thickness of strip. As for the speed ofstrip V, values which have already been measured (such as the speed atthe last stand of the finishing mill) can be utilized.

Example 3 By the method of this invention, the change of the coilingtemperature according to the increase of the rolling speed can becalculated without difficulty, as will be seen in the following.

Many of the up-to-date types of hot strip mills are so devised as tospeed up rolling of strip after the top of strip has coiled around thecoiler mandrel. This is to raise operation efficiency and improve thequality of the product.

At a certain plant, the rolling of strip of 2.3 mm. thick and 3 feetwide is carried out at the initial velocity (V of 1700 f.p.m. and at anincreased velocity of 2700 fpm. after the top of the strip has coiledaround the collar mandrel. Details of the water showering apparatus ofthe hot-run table used at that plant are not known to us. Butcalculation was made on the rise of the coiling temperature due to a1000 f.p.m. increase of the rolling velocity from 1700 f.p.m., assuming870 C. of the temperature at the outlet from the finishing mill, 600 C.for the initial coiling temperature and water shower being carried outthroughout the whole length of the hot-run table, as

6 x=heat transfer coefficient between steel strip and cooling liquid(Kcal./m. /hr. C.) T=cooling time by liquid (hr.) and equals L/V in m.follows: 5 m./hr. K1=1510 2. A method as claimed in claim 1 in which thesteel strip is cooled by radiation on the remainder of the 1510/(2..;2100) O 3 O 2 e 0 3 0 690 0 length of the hot run table according to theformula: Therefore, the coiling temperature will rise by 90 C. with 10 14 3 K T 1 the above increase of the rolling speed but with the other 3 hT 3 water showering conditions remaining the same. Wham.

Determination of the location and pressure of a water m shower forcontrolling change of the temperature oc- =temperature of steel stripbefore cooled by radiacurring while and after speeding up the rollingspeed, tion K.) can be made without difficulty by using the Formulae=temperature of steel strip after cooled by radia 2 (or 3) and 5. tionK.)

TABLE 1 a (KeaL/mfl 90 C e 0.

hr. C.) [2 (mm.) L1 (In) Lg (m.) V (f.p.m.) 91? 0.) actual calculatedtemperature temperature 9. 0 50 30 660 890 650 645 9. 0 50 30 750 900670 675 14s 9. 0 50 30 800 890 670 679 Water Shower 6. 0 50 30 720 870570 565 Pressure 10 at 6. 0 50 30 750 870 575 573 3. 2 40 40 1, 100 870580 560 2. s 40 40 1, 180 355 520 530 2. s 30 50 1, 200 840 560 580 e. 0s0 700 855 600 603 97 6.35 60 20 750 860 630 628 Water Shower 6.35 70 10690 890 620 606 Pressure 4.5 at 4. 76 5o 860 845 615 612 4. 0 40 960 870640 654 3. 2 so 0 1, 100 8 5 480 490 NoWater 2.3 0 so 1,600 865 750 745Showering 1. 6 0 s0 1, 550 820 660 670 What we claim is:

1. A method of cooling steel strip being rolled, comprising moving thesteel along the hot run table of a continuous hot strip mill for adistance L at a velocity V, and applying a shower of cooling liquid tosaid steel strip along at least a part of the length .of said hot runtable for cooling the steel from a temperature of said steel strip atthe start of said part of the length to a desired lower temperature atthe end of said part of said length and controlling the amount andpressure of cooling liquid applied by said shower to achieve a heattransfer coefiicient between the steel strip and cooling liquidaccording to the formula:

wherein 9 =temperature of steel strip before cooled by liquid 0=temperature of steel strip after cooled by liquid 0 =temperature ofcooling liquid C.)

e=base of natural logarithm C=specific heat of steel strip (Kcal./kg.C.)

specific weight of steel strip (kg./Nm.

h=thickness of steel strip (111.)

n=surrounding temperature coefficient a=emissivity of steel stripsurface T=cooling time by radiation (hr.)

lz=thickness of steel strip (m.)

C =Stefan-BaltZmann constant; 4.88 Kcal./m. hr.

C=specific heat of steel strip (KcaL/kg. C.)

=specific weight of steel strip (Kcal./Nm.

References Cited UNITED STATES PATENTS 2,696,823 12/1954 Scott 72200CHARLES W. LANHAM, Primary Examiner.

A. RUDERMAN, Assistant Examiner.

